Robertson and Peck's data published in 1974 on the thermal conductivity of Hawaiian basalts are unique in the sense that the vesicularity of the samples used for the study covers a wide range of 2 to 98%. The data consist of the measurement results of thermal conductivity on 61 samples of basalt collected from Kilauea and other volcanoes in Hawaii. The thermal conductivity was measured by the method of thermal stacking, on samples with their pores filled first with air and then with water. Thus the data are particularly suitable for evaluating the theoretical formula describing the thermal conductivity of fluid-saturated porous rock. In the formula for the thermal conductivity of a two-phase material the thermal conductivity of the solid matrix is an essential parameter, which Robertson and Peck determined by the wet cell method. The result of their determination was that they could not represent the data in the whole range of sample porosities with a single theoretical formula. This paper proposes that the thermal conductivity of the solid matrix can be estimated by extrapolating the data to zero porosity. For the extrapolation, either Fricke-Zimmerman's or Schulz's formula of thermal conductivity for a two-phase material having spheroidal inclusions can be used. In both models, for the results of extrapolation from the air-saturated and the water-saturated sample thermal conductivities to be identical, the spheroid's aspect ratio is assumed to be around 1/10. This is considered to be a combined effect of the spherical pores and the microcracks in the basalt samples. With the assumed aspect ratio of the spheroidal inclusions, either of the theoretical formulae agree with the data with sufficient precision. ¿1991 American Geophysical Union